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UGC NTA NET JRF Paper 1 (Teaching and Research Aptitude Book)

Chapter 5 Logical Reasoning (UGC NTA NET JRF Teaching and Research Aptitude Book)

Introduction

Reasoning is an important section in aptitude tests and students need to master it necessarily. They aim to check our thinking capability. We always seek explanation of objects, events, subjects and phenomena that occur around us. To seek accurate explanation, we have to apply logic. Then, what is logic? Logic is applying principles of reasoning to obtain valid inferences.
Logical reasoning is largely about adopting complete rational approach to solve a problem, with no chance for ambiguity.
On the contrary, analytical reasoning is the act of carefully considering a problem, claim, question, or situation in order to determine the best solution. Applying analytical reasoning also means seeing things from your view point, and there may be some subjectivity also. The purpose of using reasoning skills is to always justify your decisions and actions. The first part of the unit deals with logical reasoning and the second part deals with analytical reasoning.
In Unit II, on research aptitude, we have seen that there are basically two approaches to solve a problem, such as inductive and deductive. Continuing with the same idea, reasoning is basically of two types, such as deductive and inductive.
Let’s look at some of the following concepts. They are important to be understood by us. In the study of logic we come to recognize our own native capacities, and practice to sharpen them. It helps us to reason well by becoming aware about the principles of correct reasoning. The word ‘logic’ comes from the Greek word logos, literally meaning, word, thought, speech, reason, energy and fire. Logic is the science that evaluates arguments. Ancient Indians, Arabs and Chinese made significant contributions to the growth and development of logic. However, our study is restricted logic developed by Europeans over several centuries.
An argument is a group of statements including one or more premises and one and only one conclusion. Traditionally arguments have been classified into two types, namely deductive and inductive arguments.
A statement is a sentence that is either true or false, such as ‘The cat is on the floor’. Many sentences are not statements, such as ‘Kindly close the window’. A premise is an argument that provides some basic reason or support to get the conclusion. There can be one, two or many premises in a single argument. A conclusion is an argument that indicates – what the arguer is trying to convince the reader or listener. What is the argument trying to prove? There can be only one conclusion in a single argument. Inference can be valid or invalid. If inference has its basis in implication, then it is valid. On the other hand, if it does not enjoy the support of implication, then it is invalid.
Deductive Reasoning
Premise: All dogs have long ears.
Premise: Hound is a dog.
Conclusion: Therefore, Hound has long ears.
In deductive reasoning, conclusion is guaranteed to be true if the premises are true. Therefore, in the deductive inference, the conclusion cannot be more general than premise(s). Given the premises that all dogs have long ears and Hound is a dog, it is logical to assume that Hound has long ears. After all, in this example, having long ears are an inherent quality of dogs. This argument is valid. Does it mean it is also true? The conclusions are based on the premises and one of the premises is not true, it follows that the conclusion is not true, even though it is valid. If one of the premises is not true, then the conclusion is also not true.
Deductive inference is further categorized into immediate (where conclusion is drawn from a single statement) and mediate (where conclusion is drawn from two statements, called syllogism). Syllogism has been discussed further in this unit.
Deductive is akin to analysis (separating any material or abstract entity into its constituent elements).

Inductive Reasoning

Inductive reasoning is the process of making generalized decisions after observing, or witnessing, repeated specific instances of something. Inductive reasoning, while not 100% accurate 100% of the time, is still a relatively quick way to make decisions. Sometimes, saving time is as important as being accurate.
Over the course of our lifetime, we have witnessed hundreds of instances when animals eat, whether it is a cow, an elephant, or a horse. Inductive reasoning tells us that all animals must eat to survive. Have we ever witnessed every animal on earth eat? Of course, the answer is no.
However, by basic biology and common experience, we know that all animals must eat to survive. That is called inductive reasoning. Inductive is akin to synthesis (combining parts to form a whole). The following example also help in differentiating between deductive and inductive reasonings.
Deductive Reasoning
Statement I: All vegetables contain vitamins.
Statement II: Carrot is a vegetable.
Conclusion: So carrot contains vitamins.
Types of syllogism: On the basis of proposition, syllogism is of four types and they are as follows.
1. Categorical: Here, the relationship between the subject and the predicate is without any condition.
Example: I. All trains are planes. II. All dogs are animals.
Within syllogism, our focus is on categorical syllogism.
2. Hypothetical: The relationship between the subject and the predicate is asserted conditionally.
For example, if it rains he will not attend.
3. Disjunctive: In a disjunctive proposition, the assertion is of alteration.
Example: I. Either he is courageous or he is strong.
4. Relational: Here, the relation between the various terms is shown in an order: Example: a > b > c > d; so a > d (conclusion).
Inductive Reasoning
Statement I: Most vegetables contain vitamins.
Statement II: Carrot is a vegetable.
Conclusion: So carrot contains vitamins.
Following types of questions appear regularly in the NET Exam. Candidates need to go through Previous Years’ Papers section for more such questions.
1. In a deductive argument, conclusion is (a) Summing up of the premises.
(b) Not necessarily based on premises.
(c) Entailed by the premises.
(d) Additional to the premises.
Option (c) is the correct one.
2. Inductive reasoning is based on or presupposes (a) Uniformity of nature (b) God created the world (c) Unity of nature (d) Laws of nature Option (a) is the correct one. The analytical method to solve syllogism problems has been discussed in the later part of the chapter.

Structure Of Arguments

An argument, in general, is a form of communication that tries to persuade its audience to adopt a particular position about a topic. Arguments have three main parts, such as a claim that states the position to be argued; reasons that logically explain why the claim should be accepted and evidence that supports the reasons with facts, anecdotes, statistics, expert testimony, and examples.
Reasoning has to be systematic and logical. There are two main components of reasoning, such as arguments (also known as premises, statements, or propositions) and conclusion. Structure of arguments deals with basic terms, validity of arguments, converting sentences into their logical form depending on the requirement, and then application of rules follows so as to arrive at a conclusion. In previous NET examinations, many questions have been asked about basic concepts and terms relating to structure of arguments, so candidates should be well versed with these concepts and terms before they attempt practical problems.

Validity of Arguments

Deductive arguments may be either valid or invalid.
If an argument is valid, it is a valid deduction, and if its premises are true, the conclusion must be true.
A valid argument cannot have true premises and a false
conclusion. The validity of an argument depends, however, not on the actual truth or falsity of its premises and conclusion, but solely on whether the argument has a valid logical form or not. The validity of an argument is not a guarantee of the truth of its conclusion. Under a given interpretation, a valid argument may have false premises that render it inconclusive. The conclusion of a valid argument with one or more false premises may be either true or false. The following question was asked in June 2009 NET Exam.
A deductive argument is valid if (a) Premises are false and conclusion is true.
(b) Premises are false and conclusion is also false.
(c) Premises are true and conclusion is false.
(d) Premises are true and conclusion is also true. The answer is (d).
Logic seeks to discover the valid forms, the forms that make arguments valid. A form of argument is valid if and only if the conclusion is true under all interpretations of that argument in which the premises are true.
Since the validity of an argument depends solely on its form, an argument can be shown to be invalid by showing that its form is invalid. This can be effected by giving a counterexample of the same form of argument with the given premises that are true under a given interpretation, but a conclusion is false under that interpretation. In informal logic, this is also called a counterargument.
Certain examples would help in better clarification about validity of arguments.
1. Some Indians are logicians and therefore, some logicians
are Indians.
Valid argument: It would be self-contradictory to admit that some Indians are logicians but deny that some (any) logicians are Indians.
2. All Indians are human and all humans are mortal
and therefore, all Indians are mortal.
Valid argument: If the premises are true, the conclusion must be true.
3. Some Indians are logicians and some logicians are
tiresome and therefore, some Indians are tiresome.
Invalid argument: For example, the tiresome logicians might all be Chinese.
4. Either we are all doomed or we are all saved; we are
not all saved and therefore, we are all doomed.
Valid argument: The premises entail the conclusion.
Remember that this does not mean the conclusion has to be true; it is only true if the premises are true, which they may not be. The following examples would help to clarify this aspect about structure of arguments.
Premises I: Some men are lawyers.
II: Some lawyers are rich.
Conclusion: Some men are rich. This argument is invalid. There is a way where you can determine whether an argument is valid and give a counterexample with the same argument form.
Note: Logical strength and soundness are properties of arguments. Truth (or falsity) is a property of statements (or premises or conclusions). Never say that ‘argument is false’ or that ‘premise is logically strong’.
What is a counterexample? In logic, a counterexample is an exception to a proposed general rule. For example, ‘All students are lazy’ makes the claim that a certain property (laziness) holds for all students, even a single example of a diligent student will prove it false. Thus, any hardworking student is a counterexample to ‘all students are lazy’. More precisely, a counterexample is a specific instance of the falsity of a universal quantification. Structure of logical argument is based on (a) Formal validity (b) Material truth (c) Linguistic expression (d) Aptness of examples The correct answer is (a). As discussed, an argument is valid if and only if truth of its premises entails the truth of its conclusion, and each step, sub-argument, or logical operation in the argument is valid.
Analogous arguments: These are basically inductive reasoning. The analogies are not the arguments.
However, analogies are mostly used in those arguments. To argue by analogy is to argue that because two things are similar – what is true of one is also true of the other also. Such arguments are called ‘analogical arguments’ or ‘arguments by analogy’. For example, like the Earth, Europa has an atmosphere containing oxygen; it means that there might be life on Europa because it has an atmosphere that contains oxygen just like the Earth.
In December 2009 Exam, the following question has been asked.
Which of the following is an analogous statement? (a) Man is like God.
(b) God is great.
(c) Gandhi is the father of the nation.
(d) Man is a rational being.

Proposition

A proposition is a sentence that makes a statement and gives a relation between two or more terms. In logical reasoning, any statement is termed as a proposition.
A proposition is assumed to be true and from which a conclusion can be drawn. The statement, ‘All cats are lemons’ is assumed to be true as a proposition (or premise), but actually we all know that cats and lemons are entirely different entities.
Proposition consists of the following four parts:
1. Quantifier: All, no, and some. They specify a quantity. ‘All’ and ‘no’ are universal quantifiers and ‘some’ is a particular quantifier.
2. Subject (S): About which something is being said.
3. Predicate (P): Something that affirms or denies about the subject.
4. Copula: Relation between subject and predicate.
Quantifier + Subject + Copula + Predicate Examples:
All bats are boys Some players are doctors.
Quality: Categorical propositions can have one of the two qualities, such as affirmative or negative that has been clarified through ‘classification of proposition’.
Classification of Propositions
Propositions are basically of two types, namely universal and particular. Universal proposition is further divided into two parts.
1. Universal positive or affirmative (A): It denotes inclusion.
Form: All S is P, where S is the subject and P is the predicate.
Example: ‘All cats are animals’. It is basically about inclusion.
Distribution: It distributes the subject only. In the above statement, cats are distributed in animals. Predicate is not interchangeable with the subject while maintaining the validity of a proposition. We cannot say that all animals are ctas.

2. Universal negative (E): It denotes exclusion.
Form: No S is P.
Example: ‘No fish are birds’ would be a universal negative.
Distribution: Both subject and predicate. Here, an entire class of predicate term is denied to the entire class of the subject term.

Particular proposition: A particular proposition can also be divided into two parts.
1. Particular positive (I): It denotes ‘partial inclusion’.
Form: Some S is P.
Example: Some men are foolish.
Distribution: Neither the subject nor the predicate. In the example, subject term, men is used not for all but only for some men and similarly, the predicate term, foolish is affirmed for a part of subject class. So, both are undistributed.

2. Particular negative (O): It denotes partial exclusion.
Form: Some S is not P or not every S is P.
Example: ‘Some birds are not carnivores’.
Distribution: Only of predicate. will help the candidates in comparing major aspects of different forms of a proposition.
Types and Main Characteristics of Propositions

SignStatement formExamplesQuantityQualityDistributed
AAll S are PAll politicians are liarsUniversalPositiveOnly subject
ENo S are PNo politicians are liarsUniversalNegativeBoth subject and predicate
ISome S are PSome politicians are liarsParticularPositiveNeither subject nor predicate
OSome S are not PSome politicians are not liarsParticularNegativeOnly predicate

Parts Of Categorical Propositions

There are three parts of statements in categorical syllogism, such as major premise, minor premise and conclusion. Each of the premise has one term in common with the conclusion.
Parts Example
Major premise – All humans are mortal
Minor premise – All Greeks are humans
Conclusion – All Greeks are mortal
1. Major premise: Predicate of the conclusion is called as the major term. The premise containing major term is called major premise. In the example, mortal is the major term.
2. Minor premise: Subject of the conclusion is called minor term. The premise containing minor term is called minor premise. In the example, Greeks is the minor term.
3. Middle term: One term common in both the premises is called middle term. It is not a part of conclusion.
In the example, humans is the middle term.
For practical purpose, we can put the statements in the following form.
Statement 1: A B B C
Conclusion: A C According to our above discussion, A is the minor term, C is the major term and B is the middle term.
4. Conclusion: In conclusion statement, first term or (subject) is the subject of the first proposition and second term (or predicate) is the predicate of the second proposition. Types and Main Characteristics of Propositions
Sign Statement form Examples Quantity Quality Distributed
In logical reasoning or syllogism problems, the common language sentences may have to be converted into their logical form before we apply logic rules on them to draw a conclusion. For example, in a previous NET examination, statements (i) ‘only graduates are eligible for this post’ and (ii) ‘most rickshaw pullers are graduates’ were given. These types of statements need to be converted to their logical form, i.e., quantifier + subject + copula + predicate, as discussed earlier. The rules of reduction help in solving these problems. The rules of reduction can help in solving these types of questions.
1. A-type propositions: Statements starting with words ‘each’, ‘every’, ‘any’, etc., are to be treated as A-type propositions (starting with all).
Original sentence Logical form

Original sentenceLogical form
Every man is liable to commit errorAll men are persons who are liable to commit mistakes
Each student participated in the eventAll students are persons who participated in the event
Any one of the Indians is laboriousAll Indians are laborious
Only Indians are students of this collegeAll students of this college are Indians
The honest alone are successfulAll successful persons are honest

Note: Sentences with singular term or definite singular term without the sign of negation are also to be treated as A-type proposition. For example, Ram is mortal.
Converting Common Language Statements into their Logical Forms
(Continued) 2. E-type propositions: Sentences with singular term or definite singular term with the sign of negation are to be treated as E-type propositions. Sentences beginning with the words like ‘no’, ‘never’, and ‘none’ are to be treated as E-type propositions.
‘Never men are perfect’ is ‘No men are perfect’ in its logical form.
3. I-type propositions: Affirmative sentences with words like ‘a few’, ‘certain’, ‘most’, and ‘many’ are to be treated as I-type propositions.

SentenceLogical form
A few men are presentSome men are present
Most of the students are laboriousSome students are laborious
Few men are not selfishSome men are selfish
Certain books are goodSome books are good
Many Indians are religiousSome Indians are religious
All students of my class, except a few, are well preparedSome students of my class are well prepared
The poor may be happySome poor people are happy

4. O-type propositions: A negative sentence that begins with a word like ‘every’, ‘any’, ‘each’, or ‘all’ is to be treated as an O-type proposition.

SentenceLogical form
Every man is not richSome men are not rich
Certain books are not readableSome books are not readable
Most of the students are not richSome students are not rich
Some men are not above temptationFew men are above temptation

5. Exclusive proposition (a) In exclusive propositions, the subject is qualified with words like ‘only’, ‘alone’, ‘none but’, or ‘no one else but’.
(b) Here, the quantity is not explicitly stated.
(c) They can be reduced to A, E, or I types by first interchanging the subject and the predicate, and then replacing the words like ‘only’ or ‘alone’ with ‘all’.
If the exception is definitely specified as in case of, ‘All metals except mercury are solid’, then the proposition is to be treated as universal (All non-mercury metals are solid.). In case, the exception is indefinite, as in case of, ‘All metals except one is solid’, the proposition is to be treated as particular. The nature of proposition depends upon context also. For example, ‘Students are present’ is reduced to, ‘Some students are present’ (I type).
In certain cases, the predicates are qualified by words like ‘hardly’, ‘scarcely’, ‘seldom’, but quantity is not specified. Such propositions should be treated as particular negative. For example, ‘Businessmen are seldom honest’ is an irregular proposition. It is reduced to, ‘Some businessmen are not honest’.
If such a proposition contains the sign of negation, then this proposition is to be treated as an I-type proposition.
For example, ‘Businessmen are not seldom honest’ is to be reduced to ‘Some businessmen are honest’, which is an I type proposition. This is so because it involves a double negation which is equivalent to affirmation.

Deductive Inference And Syllogism

As we discussed earlier, deductive inference problems are basically of two types, namely immediate inference and mediate inference.

Immediate Inference

Here, the conclusion is drawn only from one given proposition. Two important cases of immediate inference have been discussed as given below.
1. By implication: If a given proposition is A type, then it also implies that I type conclusion must be true.

StatementImplication of statement
All chairs are tables (A type).Some chairs are tables (I type).
No chair is table (E type).Some chairs are not tables (O type).

Looking at the proposition again, when we say that ‘All chairs are tables’, it implies that ‘Some chairs (we are presently concerned with) are tables’. This is based on our knowledge that some is a part of all.
Similarly, we can say that an E-type proposition also implies an O-type conclusion. If we say that ‘No chair is table’, we are absolutely sure that ‘Some chairs are not tables’. The immediate inferencing by implication is quite similar to the concept of sub alternation also discussed under Squares of Opposition.
2. By conversion: First of all, let us be familiar with few terms.
Convertend: The original proposition Converse: The new proposition Conversion: The process itself The process consists of two steps. The first step is interchanging the subject and predicate, the subject will become the predicate, and predicate will become the subject. The second step is to change the type of the given proposition to the pattern given in Table 6.2. These conversion rules are helpful not only for immediate inference but also for mediate inference, depending on the nature of the problem and answer choices. Thus, candidates are expected to learn the conversion rules by heart.
Important note: In NET examination, many times the question is asked only about conversion.
Conversion Table

Types of StatementsValid Conversion
Universal Positive (A)
All chairs are tables.
Only Particular Positive (I)
Some tables are chairs.
Some chairs are tables.
Universal Negative (E)
No chairs are tables.
Universal Negative (E)
No tables are chairs.
Particular Positive (I)
Some chairs are tables.
Only Particular Positive (I)
Some tables are chairs.
Particular Negative (O)
Some chairs are not tables.
No conversion

For example, what can be concluded from the given statement, ‘Some men are honest’. Which of the following is true? (a) Some honest people are not men.
(b) All honest people are not men.
(c) Some honest people are men.
(d) None of the above Solution: This statement is particular positive statement.
Hence, according to Table 6.3, it can be converted into PP only.
Answer Choices and Justification as per
Conversion Table

Answer choicesJustification
(a) Some honest people are not men.Particular Negative, hence eliminate.
(b) No honest people are men.Universal Negative, hence eliminate.
(c) Some honest people are men.PP, hence this is correct answer.
(d) None of the aboveNot applicable because C is the correct answer.

Mediate Inference

There are basically two approaches to solve a syllogism problem, namely (i) analytical method and (ii) Venn diagram.
Most of the candidates prefer Venn diagram method to analytical method as they find it easier.
In this book, there are many illustrations using both the methods. As many times the questions are asked from analytical method in NET examination, the candidates should be well versed with analytical method as well. Here, we have focused mainly on the analytical method with Venn diagram just as a supplementary solution.
Candidates are advised not to rely exclusively on Venn diagrams as they can be ambiguous at times. As many questions based on theory are expected, analytical method can reinforce our understanding about the concepts.

Analytical Method for Mediate Inference Problems

The basic steps to solve syllogism problem are (i) the alignment of statements and (ii) drawing conclusions.
Depending on the nature of the problem, it can entail two additional steps also.
shows the steps needed in analytical method for mediate inference.
Steps in Analytical Method for Mediate Inference
Problems

Step IAlignment of the propositions— standard format
Step IIDraw conclusion by use of table
Step IIICheck for immediate inferences
Step IVCheck for complementary pair if steps II and III fail

It consists of two steps, so initially, make sure that there are exactly three terms given in both the statements. In case, the number of terms is different, we need not go further, as there will be no conclusion. Secondly, we check whether the propositions are in standard form or not.
For practical purposes, the following format can be used as a standard.
Minor (or first) term A→B Middle term (major or third) term B→C A, B and C used above denote the first, second and the third term, just for quick representation of terms while solving practical questions. Please note that this A (used for first term) is different from A used for universal affirmative.
As discussed earlier, in the conclusion statement, first term (subject) is the subject of the first proposition and second term (predicate) is the predicate of the second proposition. This fact becomes the basis for the alignment of propositions.
In case, the problem is in the standard form, we can directly move to Step II.
If one or both propositions are not given in the standard format, align them by (i) converting the first or second statement or both and (ii) changing the order as will be clear through the following examples.
Note: It is important to remind at this stage that sometimes the words ‘mostly’, ‘generally’, ‘only’, and so on are mentioned in one or both the statements. Initially, we convert them into logical form before doing their alignment, if required. This has been discussed separately under ‘Converting common language statements into their logical Form’ on Page 6.5.
Example 1 Statements
1. Intelligent alone are laborious.
2. Most of the girls are smart. These statements should first be converted into logical forms according to the rules for logical form.
1. All smart are laborious. This is in the form B to C.
2. Some girls are intelligent. This is in the form A to B.
Just by changing their order, we can align them. After alignment is done, we move to Step II.
Example 2 Statements
1. Some pens are books.
2. Some stationery are books.
As books are the common term, they are in the form A to B and C to B. The first statement does not require any change. As the second statement is in particular positive (I type), this can be changed to I type only according to conversion table given earlier. The second statement will become, ‘Some books are stationery’.
Now, propositions are properly aligned, i.e., ‘Some pens are books’ and ‘Some books are stationery’. We now move to Step II.
Example 3 Statements
1. No van is house.
2. All boxes are house.
Here, the common term, house, is the predicate in both propositions. Here, we have to alter the first proposition and also change the order to bring it to the form A to B and B to C.
1. All boxes are house.
2. No house is van.
Now, the predicate of first proposition is the subject of the second statement.
Example 4 Statements
1. All boys are tigers.
2. Some tigers are coward.
Solution: Here, the middle term, tiger, is the predicate in first proposition and the subject of the second proposition.
No alignment is required.
After aligning the statements among themselves, we can move to Step II. There can be confusion while aligning a pair of statements, where the statement should be given priority in terms of conversion. For example, if there are two statements, A type and I type, which should be converted so that our purpose of getting the standard form is achieved. The IEA rule helps in such decision-making.
If first statement given is of A type and second is of I type, then as per IEA rule, I type statement should be given priority for conversion. Similarly, in case of confusion between E type and A type, E type should be given priority over A type.
IEA Rule
Step II: Applying Syllogism Rules
After ensuring that propositions are in a standard format, we apply syllogism rules to draw conclusions.
After aligning the statements, as per our discussion in Step I, conclusion may be drawn by using
where the rules of syllogism are mentioned.
No definite conclusion can be drawn for other combinations like A + I or O + A, which have not been mentioned in the above table. In general, we can say that two negatives (E + E, E + O, O + E, or O + O) do not lead to any conclusion. Two particulars also do not lead to any conclusion.
Statements: I. All chairs are tables. (A type) II. All tables are furniture (A type) Conclusion:
All chairs are furniture. (A + A = A).
Now, consider Example I as discussed in Step I.
1. Some pens are books. (I type) 2. Some books are stationery. (I type) No conclusion as I + I = No conclusion.
Now, consider some examples from NET previous years’ exams. In each of the following questions (1–3), two statements are followed by two conclusions, A and B. Assuming that the given statements are true even if they are at variance with commonly known facts, pick up one of the following answer choices which you think is correct.
(a) If only conclusion A follows.
(b) If only conclusion B follows.
(c) If both A and B follows.
(d) If neither A nor B follows.
Question 1 Statements
1. Some doctors are fool.
2. He is a doctor.
Conclusions A. He is a fool.
B. Some fools are doctors.
Solution
No conclusion can be drawn from the two particular affirmative propositions. So (A) does not follow.
Second conclusion is the converse of first statement, so (B) follows. Hence, (B) is the answer.
Question 2 Statements
1. All birds are men.
2. All crows are birds.
*In this case, the flow is from C to A, and not from A to C as in all other cases. (Please refer Table 6.5. A, B, and C stand for first, middle, and
second terms, respectively.)
Rules of Syllogism

Proposition I (A to B)Proposition II (B to C)ConclusionSummarized form
Universal Positive (A)Universal Positive (A)Universal Positive (A)A + A = A
Universal Negative (E)Universal Negative (E)A + E = E
Universal Negative (E)Universal Positive (A)Particular Negative (O)E + A = O*
Particular Positive (I)Particular Negative (O)E + I = O*
Particular Positive (I)Universal Positive (A)Particular Positive (I)I + A = I
Universal Negative (E)Particular Negative (O)I + E = O

Conclusions A. All crows are not men.
B. Some men are not crows.
[June 1997 and June 2001] Explanation Step I: The middle term is birds. A close observation reflects that the statements are in the form B to C and A to B. After swapping, the statements will be ‘All crows are birds’ and ‘All birds are men’.
Step II: The conclusion should be A + A = A (universal positive). The conclusion is ‘All crows are men’. So (d) is the answer.
Question 3 Statements
1. All boats are boys.
2. All boys are lamps.
Conclusions A. All lamps are boats.
B. All boats are lamps. (December 2002)
Solution Step I: Statements are in the standard form A to B and B to C. The common term, boys, is the predicate of the first proposition and subject of the second proposition.
So no alignment is required.
Step II: A + A ⇒ A The subject of the conclusion will be the subject of first statement, and predicate of the conclusion will be the predicate of second statement. The common terms will disappear. So, the conclusion is ‘All boats are lamps’. Thus, only conclusion 2 follows and (B) is the answer.
Now solving the problem through Venn diagram solution.
According to Statement I, ‘All boats are boys’.
Boys
Boats
Figure 6.4
According to Statement I and Statement II, the Venn diagram looks as given below.
Boys
Lamps
Boats
Figure 6.5
Looking at the Venn diagram, we can say that second conclusion, ‘All boats are lamps’ is correct.
Question 4 Statements
1. All lemons are balls.
2. No bats are lemons.
Conclusions A. Some balls are not bats.
B. Some bats are lemons.
Solution
By changing the order of the statements itself, we can align the sentences. The aligned pair is No bats are lemons. So (a) is the answer All lemons are balls.
E + A = O*. So the conclusion is, ‘Some balls are not bats’.
Note: In all the questions discussed previously, Step III and Step IV are not required as per the answer choices.
Step III: Checking for Immediate Inferences
(If Required)
We can check the conclusion (or even statements) for immediate inference as per answer choices. Usually, in this case, there are more than two conclusions. Even in case of two conclusion questions, we can go for this step.
Let us discuss one comprehensive example.
Statements
1. Some tables are chairs.
2. Some chairs are furniture.
Conclusions I. Some chairs are tables.
II. Some furniture is chair.
III. All tables are furniture.
Choices
(a) I and II are valid.
(b) II and III are valid.
(c) I and III are valid.
(d) None of the above.
Solution
I + I = No conclusion (two particulars do not lead to any conclusion), but after immediate inference, we find that (i) and (ii) are valid. So, option (a) is the answer.
Step IV: Checking for Complementary Pair
(If Required)
Check for complementary pair if Steps II and III fail.
Complementary pair is a pair of contradictory statements, both cannot be true simultaneously.
We can call a pair as a complementary pair if
1. The subject and predicate of both the sentences are the same.
2. They are I + O or A + O or I + E type pairs which have been discussed below.

I + O typeA + O typeI + E type
Some chairs areAll chairs areSome chairs are
tables.tables.tables.
Some chairs areSome chairs areNo chair is a
not tables.not tables.table.

Note: Sometimes, the converse of the derived conclusions is among answer choices. To sum up all the discussion, some golden rules have emerged to solve the syllogism problems. These are in continuity with the earlier discussion.
1. Every deduction should contain exactly three terms.
2. The middle term (present in both the premises) must be distributed at least once.
3. If one of the premises is negative, then the conclusion must be negative (will have the word ‘no’ or ‘not’.
4. If one of the premises is particular, then the conclusion must be particular (will have the words ‘some’, ‘few’, ‘many’, etc.).
5. If both the premises are particular, then no conclusion can be drawn from the given premises.
6. If both the premises are negative, then no conclusion can be drawn from the given premises.
7. A term that is not distributed in the premises cannot be distributed in the conclusion.
A Snap Shot–Golden Rules of Syllogism
Comprehensive Example of Mediate and Immediate
Inference as per the CBSE UGC-NET exam Pattern
Statements
1. All movies are stories.
2. All stories are surprises.
Conclusions A. All movies are surprises.
B. Some surprises are movies.
First, let us consider only the statements. The sentences are already aligned.
Since A + A = A, the conclusion will be ‘All movies are surprises’. Till this point, it is a question of mediate inference.
If we convert this conclusion (immediate inference), we get, ‘Some surprises are movies’. Hence, both the conclusions given in the question are true.
Statements
1. Some rooms are lamps.
2. Some lamps are tubes.
Conclusions A. Some rooms are tubes.
B. Some lamps are rooms.
We know that from a combination of I + I, no conclusion can be drawn.
On converting the first statement, we get ‘Some lamps are rooms’, i.e., conclusion (B).
Also, on converting the second statement, we get ‘Some tubes are lamps’. This proposition is not given in the conclusion part. So in this example, conclusion (B) alone is true. Thus, we can see the importance of immediate inferences in solving syllogism problems.

Structure Of Arguments: Additional Concepts

There are other perspectives or dimensions of structure of arguments (relational arguments, symmetry, transitivity, reflexiveness and connexity), squares of opposition (contradictions, contraries, sub contraries, and sub alternations), definitions (stipulative, lexical, precising, operational, etc.), and other terms such as prejudices, facts, opinions and advice that suggest more about the structure of arguments. The questions have been asked regularly in NET paper examination. The types of questions have been mentioned during the course of discussion as well as in practice questions theory. Candidates are expected to go through these topics. There is one example taken from NET previous years’ paper.
Example In the expression, ‘Nothing is larger than itself’, the relation ‘is larger than’ is (a) Antisymmetric (b) Asymmetrical (c) Intransitive (d) Irreflexive

Relational Arguments

In relationship arguments, both premises and their conclusions are relational proposition. There are two characteristics of a relation—relation to itself and to others. Deductive reasoning is also sometimes dependent on the validity of relational arguments. In NET examination, questions have been asked on relational arguments. These are quite easy to understand.

Classical Square of Opposition

The categorical propositions having same subject and predicate terms may differ in quality and quantity or in both. This differing is called opposition. There were few questions in previous years’ exams, where understanding terms, such as contradictory, contrary, subalternation and subcontrary may help in finding solutions.
By which of the following propositions, the proposition, ‘Some men are not honest’ is contradicted? (a) All men are honest.
(b) Some men are honest.
(c) No men are honest.
(d) All the above
1. Two propositions that have the same subject and predicate terms but different in quality are (a) Contradictory (b) Contrary (c) Subaltern (d) Subalternation [June 2008] 2. ‘No men are mortal’ is contradictory to (a) Some men are mortal.
(b) Some men are not mortal.
(c) All men are mortal.
(d) No mortal is man. The understanding of squares of opposition can help candidates in attempting these types of questions.

1. Contradictories: Contradictory opposition is the relation between two propositions having the same subject but differing in both quality and quantity. The relation between A and O and E and I is called contradictory.
A O
E I

A typeO type
All diamonds are precious stones.Some diamonds are not precious stones.
All men are honest.Some men are not honest.

E typeI type
No diamonds are precious stones.Some diamonds are precious stones.
No men are honest.Some men are honest.

In order to refute the truth of the proposition ‘All men are honest’, it would be enough to show that some men (or even one man) are not honest. One exception would disprove the truth of the universal affirmative proposition.
Classical Square of Opposition
(Continued) 2. Contraries: Contrary opposition exists between two propositions when both have universal quantity but one affirms and the other denies its predicate of the subject. The relationship between A and E is called contraries.
A E
Examples
(A) All men are honest. (E) No men are honest.
(A) All judges are lawyers. (E) No judge is lawyer.
3. Sub contraries: The relation between two particular propositions having the same subject and predicate but differing in quality is subcontrary opposition. The relation between particular affirmative (I) and particular negative (O) is called subcontraries.
I O
Example: I: Some judges are lawyers. O: Some judges are not lawyers.
4. Sub alternation: Sub alternation opposition is the relation between two propositions having the same subject and predicate but differing in quantity only.
If universal is true, then particular must be true. What is true about the whole population, is true about its part also. If universal is false, then particular may be undecided. The relation between ‘A and I’ and ‘E and O’ is called subalternation.
A I
E O
A: All Indians are spiritual. I: Some Indians are spiritual.
E: No Indians are spiritual. O: Some Indians are not spiritual.

ContradictoryContrary
(a) If one is true, then the other will be false definitely.(a) Its always between universal.
(b) If one is false, then the other will be true definitely.(b) Both statements cannot be true at the same time but both can be false.
(c) Both cannot be true or false at the same time.(c) If one is true, then the other will be false definitely.
(d) If one is false, then the other will be doubtful.
Sub-ContrarySubalternation
(a) Its always between particular.(a) Between universal and particular.
(b) Opposite to contrary.(b) If universal is true, then particular will be true definitely.
(c) Both statements cannot be false at the same time but both can be true.(c) If universal is false, then particular will be doubtful.
(d) If one is false, then the other will be true definitely.(d) If particular is false, then universal will be false definitely.
(e) If one is true, then the other will be doubtful.(e) If particular is true, then universal will be doubtful.
(f) Truth donwward, false upward.

 
Symmetry
1. Symmetrical relationship Example
A is equal to B.
So, B is equal to A—valid.
It is a ‘symmetrical relationship’.
2. Asymmetrical relationship Example
A is greater than B.
So, B is greater than A—invalid.
3. Non-symmetrical relationship Example
A is the sister of B.
So, B is the sister of A—may or may not be valid.
B may be the brother of A. Transitivity
1. Transitive relation: It implies that a relation travels from A to C through B.
Example
A is equal to B.
B is equal to C.
So, A is equal to C—valid.
In transitive relations, the premises are true and conclusion is also valid. ‘Younger to’, ‘precedes’, ‘succeeds’, and ‘ancestor of’ are other examples of transitive relationships.
2. Intransitive relation: Here, relation does not travel from A to C through B.
Example
A is the father of B.
B is the father of C.
So A is the father of C—invalid (false conclusion) Relations such as ‘son of’ also fall in the category of intransitive relations.
3. Non-transitive relation: Example
A is an enemy of B.
B is an enemy of C.
So, A is an enemy of C—invalid or false conclusion. The relations such as ‘friend of’ and ‘neighbour of’ are examples of non-transitive relationships.
Reflexiveness
1. Reflexive relationship is between a term and itself.
Some examples are, ‘is equal to itself, ‘resembles itself’, ‘as old as’, and ‘as young as’.
2. Partial reflexiveness means establishing a relationship with some other thing. Its examples are, ‘A is as tall as B; B is as tall as C’. Hence, A is as tall as B.
3. Irreflexive: This type of relationship cannot be held between a term and itself. A is smaller (or greater) than itself. A is west (or east) of itself, and so on.
4. Non-reflexive: This may or may not be held between a term and itself. An example is, ‘A loves itself’. This may or may not happen.
Connexity
This type of relationship is valid between any two terms. For example, 3 is greater than 2 but less than 4.

Types of Definition

A definition is a comprehensive description of a concept by means of known concepts expressed mainly by verbal means. The purpose of a definition is as follows.
1. To describe a concept at a given level of abstraction.
2. To distinguish a concept from related concepts.
3. To establish a relationship between the concept in question and the other concept in order to determine the position of the concept in the system.
4. To delimit a concept for the purpose of normative terminological work. The definition should be the starting point for selecting and analysing the term. When selecting or seeking an appropriate term for a concept, it is necessary to start with a clear definition of the concept. For clarifying the concept, its intension and its extension have to be determined.
In NET examination, many times questions have been asked on the definition of the following terms.
1. Intensional definition: Specifying the properties or features and also the meaning of a term. For example, water in chemistry is defined as a compound of hydrogen and oxygen and in physics as a liquid with freezing point of 0°C and boiling point of 100°C.
2. Extensional definition: Specifying the class members of the term. For example, the planets of the solar system are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto.
3. Lexical definition: It is also termed as reportive definition. Lexical definition is the dictionary meaning of a term, the common vocabulary of a given language, for example, defining book, chair and so on.
4. Stipulative definition: It is an arbitrary, specified definition. It is not used to explain the existing meaning of a term. It is used to assign a new meaning to a term, whether or not the term has already got a meaning. Some examples are idioms and slangs used in English language.
5. Precising definition: A definition developed to clarify a vague or ambiguous term. It is often used in legal, scientific or medical settings. For example, a virus is an infectious agent that causes small pox.
6. Persuasive definition: A persuasive definition is any definition that attaches an emotive, positive or derogatory meaning to a term where it has none. This may be used as a rhetoric tool in a debate or discussion. For example, someone against abortion might offer the definition of ‘abortion’ as the murder of an innocent person during pregnancy. This definition carries a negative connotation, as the term murder suggests that abortion is wrongful killing and it also assumes that the aborted foetus is already a person. Such a definition is surely not appropriate in a fair debate on the moral legitimacy of abortion, even though it might be useful as a rhetorical tool.
7. Operational definition: A definition that provides a meaning to a term by specifying a measurement procedure.
8. Functional definition: A definition that specifies the purpose or use of the items denoted by the term.
9. Ostensive definition: A definition developed by showing someone an object and attaching a word to it. This type of definition is often used where the term is difficult to define verbally, either because the words will not be understood (as with children and new speakers of a language) or because of the nature of the term (such as colours or sensations).
For example, defining red by pointing out red objects—apples, stop signs, roses, etc.—is giving ostensive definition, as is naming.
10. Analogous definition: This definition has analogy; corresponding in some particular. A brain and a computer are analogous.
In biology, there is corresponding in function but of different origins and having evolved separately, as the wings of birds and insects.

Connotative and Denotative Meanings

Words are not limited to one single meaning. Most of the words do have multiple meanings, which are either categorized as denotative or connotative. The denotation of a word is its explicit definition as listed in a dictionary.
Let us consider the word home as an example. The denotative or literal meaning of home is ‘a place where one lives; a residence’. The expressiveness of a language, however, comes from the other type of word meaning, such as connotation or the association or set of associations that a word usually brings to mind. The connotative meaning of home is a place of security, comfort and family. The quote ‘East or west, home is the best’ does not refer to denotative meaning of home, but the emotions the word home evokes in most of us. By definition, synonyms have the same denotation or literal meaning, but almost always have different connotations.

Fact, Opinion, Belief, and Prejudice

In these types of questions, a statement is given, where the candidate has to answer whether the statement is a fact, a prejudice, a belief or just an opinion.
In the past, many questions have been based upon the understanding of these terms.
Statement
English is an invaluable asset in international communication.
Mark
(a) If the statement is a fact.
(b) If the statement is an advice.
(c) If the statement is an opinion.
(d) If the statement is a prejudice.
Similarly, there were statements (i) Decline of the British Empire should have resulted in the decline of English.
(ii) Persons educated through a foreign language are sure to be unpatriotic.
Facts
A fact is verifiable. We can determine whether it is true by researching the evidence. The facts are as follows.
1. Things known for certain to have happened.
2. Things known for certain to be true.
3. Things known for certain to exist. This may involve numbers, dates, testimony and so on. For example, India got independent on 15 August, 1947. Facts provide crucial support for the assertion of an argument.
Opinion
An opinion is a judgment based on facts, an honest attempt to draw a reasonable conclusion from factual evidence. Opinions are as follows.
1. Things believed to have happened.
2. Things believed to be true.
3. Things believed to exist.
For example, we know that lakhs of people go without proper medical care in India, and so someone forms the opinion that the country should institute national health insurance even though it would cost few thousand crores of rupees. An opinion is potentially changeable, depending on how the evidence is interpreted. Opinions are debatable, but facts usually are not.
Prejudice
Another kind of assertion that has no place in serious argumentation is prejudice, a half-baked opinion based on insufficient or unexamined evidence (For example, women are bad drivers). Unlike a belief, a prejudice is testable, it can be contested and disapproved on the basis of facts. We often form prejudices or accept them from others, such as family, friends, media, and so on without questioning their meaning or testing their truth.
Belief
Unlike an opinion, a belief is a conviction based on cultural or personal faith, morality or values. Statements such as ‘capital punishment is a legalized murder’ are often called opinions because they express viewpoints, but are not based on facts or other evidence. They cannot be disapproved or even contested in a rational or logical manner. Since beliefs are inarguable, they cannot serve as the thesis of a formal argument.

Analytical Reasoning

Analytical reasoning is considered to be the recent form of logic in which almost all classical terms are covered. Here, a sentence, a group of sentences, a short argumentative paragraph covering concepts, facts, theories, figures and so on may be given and questions are asked with regard to arguments, conclusion, inferences, implications and so on. In dealing with these questions, the methods generally used include inductive reasoning, deductive reasoning, quoting authorities, and facts, findings and illustrations.
Solution Approach
1. Underline the important assumptions in the case of passage. Note the inferences which are both inductive and deductive.
2. Identify the supporting arguments.
3. Note the premises of supporting argument.
4. See the nature of questions.

Nature of Questions

Based on the given information, the types of questions to be asked include the following.
1. Assumptions and statements 2. Force of argument 3. Assertion and reasoning 4. Statements (situation) and course of action Various concepts of analytical reasoning have been discussed below.
Assumptions and Statements
Assumptions are unstated or even unknown, but implied by the associated theory or argument. Thus, an assumption can be termed as an implied premise.
An assumption is defined as something which is assumed, supposed or taken for granted. In practical life, if something is to be conveyed, it is not put in words. Many things may not be said, but are taken for granted which may be defined as an assumption.
Implicit means hidden and therefore, implicit assumptions are those assumptions which are hidden. A typical question on implicit assumptions goes like: Directions (Questions 1–5): In each of the questions below, a statement is followed by two assumptions numbered as I and II. An assumption is something that is supposed or taken for granted. You have to consider the statement and the following assumptions and decide which of the assumptions is implicit in the statement.
(a) Only assumption I is implicit.
(b) Only assumption II is implicit.
(c) Both I and II are implicit.
(d) Neither I nor II is implicit.
Example 1 Statement
A to B – ‘In my opinion, you should undergo a training under an expert in order to be successful in your career’.
Assumptions I. B sought advice from A.
II. Experts are more competent to guide a person to be successful in their career.
Explanation
There are many instances in life when we get an advice from a person without asking it. I is not definitely valid.
Only assumption II is implicit. Otherwise, A would not have advised B to get training from an expert. Therefore, it is correct to assume that experienced people make better guides.
Example 2 Statement
‘This multimedia CD-ROM offers you active help as you learn yoga without an instructor’ says a newspaper advertisement.
Assumptions I. Everyone may not be able to get active help from a yoga instructor.
II. Aerobic exercises can be learnt with the help of a CD-ROM.
Explanation
In the above, both I and II are valid. The multimedia CD-ROM intends to teach yoga in the absence of an instructor. This means that the absence of an instructor is a distinct possibility for many people. Therefore, I is valid. The advertiser has come out with a CD-ROM on yoga. It definitely implies that aerobic exercises can be learnt by CD-ROMs. Hence, II is also valid.
Example 3 Statement
‘If you keep creating indiscipline in class, I will have to take a strict action against you’. A teacher warns his student.
Assumptions I. With the warning, the student may stop creating indiscipline in the class.
II. All students are basically naughty.
Explanation
The teacher warns his students in anticipation that he would stop troubling him. So I is implicit. The general nature of children cannot be derived from the statement.
So II is not implicit.
Example 4 Statement
Of all the newspapers published in India, ‘The Hindu’ has the largest number of readers.
Assumptions I. The volume of readership of all newspapers in India is known.
II. No newspaper in India other than ‘The Hindu’ has a large readership.
Explanation
It is on the basis of data that we can say that ‘The Hindu’ has the largest number of readers. So assumption I is implied. But it is not possible to say that no other newspaper in India has a large readership. We need to define large readership as well. So assumption II is not implicit.
Such decisions as given in the statement are taken only after taking the existing vacancies into consideration.
So I is implicit while II is not.
Force of Arguments
Argument: Earlier also we discussed about the validity of arguments. An argument is a set of two or more premises leading to a conclusion. An argument can be said to be valid if the premises, if true, definitely lead to a conclusion.
All scientists are intelligent people. Raman is a scientist.
So, Raman is an intelligent person (valid).
All scientists are genius. Raman is an intelligent person.
So Raman is a scientist (invalid). The second argument is invalid as there is no premise which states that all intelligent persons are scientists.
Validity is the property of an argument.
Assertion and Reasoning
Introduction: Assertion and reasoning-type questions have one assertion (A) and one reason (R). We must first determine whether the statement is true. If statement is true, we must next determine whether the reason correctly explains the assertion. There is one option for each possible outcome. These types of questions are followed by four options.
(a) A is true but R is false.
(b) A is false but R is true.
(c) Both A and R are true and R is not the correct explanation of A.
(d) Both A and R are true and R is the correct explanation of A.
Few examples have been discussed as given below.
Example 1 Assertion (A): Most of the prominent places in ancient civilizations grew near rivers.
Reason (R): Rivers provide water for irrigation and also work as means of transportation.
Explanation: Here, we can use our basic general knowledge or commonly known facts. We know that most of the ancient civilizations grew near rivers, so A is correct. In the example, R is also simple and true.
So, option (a) is the answer.
Example 2 Assertion (A): Tides indicate the regular and periodic rise and fall in sea level.
Reason (R): Tides are caused by the gravitational pull of the moon and sea level.
Explanation: In this case also, the concept of tides is the reason for their origination. Both A and R are true, so, option (c) is the answer.
Example 3 Assertion (A): Mercury is the farthest planet from the sun.
Reason (R): Mercury is the smallest planet in the entire solar system.
Explanation: Here, A is false as mercury is the closet to sun. Hence, R is the correct option.
Example 4 Assertion (A): Carbon monoxide when inhaled causes death.
Reason (R): Carbon monoxide combines with haemoglobin.
Explanation: The chemical composition of oxygen and carbon monoxide is the same. Carbon monoxide combines with haemoglobin and reaches different parts of the body and causes death. Hence, (a) is the correct answer.
Statements and Courses of Action
Introduction: A course of action is a step or administrative decision to be taken for improvement, follow- up, or further action in regard to the problem, policy and so on. On the basis of the information given in the statement or situation, the candidate has to assume everything in the statement to be true and then decide which of the suggested courses of action logically follow for pursuing.
Example 1 Situation: The incessant rains that have been continuing for past several days have created the problem of deluge, i.e., because the river bed is full of silt and mud.
Courses of actions I. The people living close to the river should be transferred to a safer place.
II. People should be given information about the imminent danger on radio or television.
III. Immediately after the reduction of water level of the river, the silt and mud should be removed from the river body.
(a) Only I and II follows.
(b) Only II and III follows.
(c) None of these follow (d) All of these follow Explanation: Actions I and II are immediately required as they are crucial in saving precious lives of the people.
It may not be practicable for authorities to remove silt and mud from the river body. So only I and II follow, and hence, (a) is the answer.
Example 2
Indicate which of the following actions are the most appropriate in the situation given below.
Situation: Two to three students in the class of a sincere and devoted teacher frequently disturb him in the class while teaching. He is fed up with them.
Courses of actions
(a) He tells the students of the class that he will not hold the classes if the disturbing students continue doing that.
(b) He suspends the disturbing students from attending his class in the interest of the whole class.
(c) He talks to the disturbing students to find out what makes them behave that way and what could become about them.
(d) He reports against them to the principal with the recommendation to take strong action against them.
Explanation: (c) suggests long-term approach to deal with the issue of indiscipline in the class.

Formal and Informal Fallacies

Fallacies are errors but can be tricks of reasoning.
Fallacy is an error of reasoning if it occurs accidentally; it is a trick of reasoning if a speaker or writer uses it in order to deceive or manipulate his audience.
A fallacy is ‘an argument, or an apparent argument, which professes to be decisive of the matter at the issue, while in reality or it is not’. Fallacies weaken arguments and in doing so, weaken the overall strength of our paragraph or assignment.
Usually, there are five common categories of fallacies and they are listed below.
1. Using feelings 2. Distracting from the argument 3. Misinformation 4. Generalisations (to make a powerful statement).
5. Irrelevant connections According to NET syllabus, fallacies are mainly of two types, such as formal or informal.
Whatever its type is, its use undercuts the validity and soundness of any argument, but fallacious reasoning may damage the credibility of the originator of message and play with the emotions of the receiver.

Formal Fallacies

Most formal fallacies are errors of logic, where the conclusion is not supported by the premises, so it does not really ‘follow from’. Either the premises are untrue or the argument is invalid. Given below is an example of an invalid deductive argument.
Premise: All black bugs are carnivores.
Premise: All rats are carnivores.
Conclusion: All rats are black bugs.
Bugs are a subset of carnivores. Rats also are a subset of carnivores. But these two subsets do not overlap, and that fact makes the conclusion illogical. The argument is invalid, i.e., the relationship between the premises doesn’t support the conclusion.
But Then How to Recognizing the Formal Fallacies?
‘Rats are black bugs’ is instantaneously recognizable as fallacious, it sounds illogical also. However, that and other forms of poor logic play out on a daily basis, and they have real world consequences. Below is an example of a fallacious argument.
Premise: All Europeans are Christians.
Premise: All Russians are Christians.
Conclusion: All Russians are Europeans. This argument fails on two levels.
1. The premises are untrue because although many Europeans and Russians are Christians, not all are.
2. The two ethnic groups are sets that do not overlap but the two groups are confused because they (largely) share one common quality.
Informal Fallacies
Informal fallacies take many forms. They are widespread in our routine lives.
Informal fallacies develop when
1. The relationship between premises and conclusion does not hold up.
2. When premises are unsound.
3. Informal fallacies are more dependent on misuse of language and of evidence.
Frequently, they may bring irrelevant information into an argument or they are based on assumptions that, when examined, prove to be incorrect, but it may not always be easy to spot them. Some moves are always fallacious and others may be allowable on the basis of context.
Use of Ethos, Logos, and Pathos to Test Arguments for
Fallacies
To test an argument for fallacies is to return to the concepts of ethos, logos and pathos.
• Ethos: For ethics, authority and/or credibility.
• Logos: An appeal to logic.
• Pathos: An appeal to emotion.
Ethos, logos and pathos can be used to strengthen our argument or inappropriately to manipulate an audience through the use of fallacies. Some fallacies may fit into multiple categories. Thus, we can see that both formal and informal fallacies are errors of reasoning, and if speaker or writer relies on such fallacies, even unintentionally, he/she undercuts their argument.

Indian Logic: Means Of Knowledge

After asking, ‘Can I know?’, the next question is obviously ‘How do I know?’ or the sources of knowledge.
Epistemology is the study of the origin, nature and limits of human knowledge.
Logic is the study of inference and argument. The logic and theory of knowledge of Indian systems are largely coloured by their metaphysical tenets.
Philosophy basically deals with interpretation of man and nature. It is the analysis, assessment and exposition of the process of knowledge.
As per Indian logic system, knowledge is first received through perception (pratyaks¸a) or comparison (upama¯na), or words of sacred authority. We will discuss them.
Here, the aim is to study Indian logic by means of knowledge.

In India, there are six orthodox schools of philosophy which recognize the authority of Vedas as divine revelation. Those who did not recognize this authority were the Jains, Buddhists (both heterodox) and Charvaka (materialists). There is much divergence of opinion among Indian philosophers concerning the nature and scope of Pramana (source of knowledge).
Indian Philosophy divides itself into three periods
1. Vedic period 2. Upanishadic period 3. Post-Vedic period The post-Vedic period is a systematic period which saw the development of ‘orthodox systems’. Currently, we are starting with Charvaka system.

Charvaka Materialist School’s Views of Knowledge

Rishi Brihaspati probably was the founder of this school.
Charvaka is also called Lokayata, the Sanskrit word for it is ‘Worldly Ones’, which is the view held by the common people.
As we discussed ‘pratyaksha’, it is the only source of valid knowledge. Only direct perception (anubhava) is recognized. What we cannot perceive through senses must be treated as non-existent. They refute all other sources of knowledge, such as no mind, no consciousness, and then no soul. Only physical body is real. There are four traditional elements of earth, water, fire and air. The validity of inference is also rejected by Charvakas. Inference is considered to be a mere leap into the dark.
We proceed from the known to the unknown and there is no certainty in this, though some inferences may turn out to be accidentally true. Induction is uncertain, and deduction is argument in a circle. Deductive inference is vitiated by the fallacy of petition principia. Though we consider invariable association or Vyapti
as the nerve of all inference, Charvakas challenges this guess work and regards it just as a guess work.
Perception does not approve this Vyapati. Inference and testimony does not approve it.
Charvaka review perception is valid and inference is invalid itself is the result of inference. The creations such as Kautilya’s Arthashastra
(Science of material gain) are based on it as it is considered to be an hedonist opportunist approach.

Orthodox Views of Knowledge

The Nyaya and Vaishesika schools are primarily analytic and are therefore, more concerned with logic and epistemology than ethics. The Nyaya School
As per NTA-NET syllabus we actually focus on Nyaya
system.
It was formed during 4th Century BCE by Gautama.
Here, the knowledge comes from perception, inference, comparison and verbal testimony.
Objects of learning are self, body, sense organs, sense objects, intellect, mind and activity.
It is an orthodox system of atomistic pluralism and logical realism. It invented a science of knowledge (Pramanasastra). If a means of knowledge is impossible, then denial of it would also be impossible. If denial is based on a means of knowledge, then the validity of means have to be acknowledged.
It has explored remarkably the domain of cognitive consciousness and determined the process by which it enters into a connection with the world of physical objects. The outside world is known to us through the senses and the mind. It believes in the external things as reflecting their real nature when knowledge is true, and their unreal nature when knowledge is false.
Knowledge is the knowledge of things, and it constitutes the expression of reality (arthhubhava).
Whatever its type, it is a natural response to the disposition present in human mind.
In the Nyaya philosophy, knowledge is termed as the manifestation of object. Knowledge lights its objects as does a lamp. Knowledge may be valid or invalid.
Valid knowledge (prama) is defined as the right apprehension of an object. It is the manifestation of an object as it is.
Nyaya maintains the theory of correspondence.
While Nyaya system recognizes all the four Pramanas, namely perception, inference, verbal testimony and comparison, Vaisesika recognizes only two Pramanasperception and inference and reduces comparison and verbal testimony to inference. The Vaishesika Philosophy
Nyaya system is allied to the Vaishessika systems, which developed metaphysics and ontology. The Vaishesika
sutras are the oldest ones, and by Kannada were written shortly before Gautama’s Nyaya Sutras. The word Vishesa means particularity and emphasizes the significance of individuals. It recognizes three real objects of experience as substance, quality and activity. There are three products of intellectual discrimination, which are generality, particularity and combination.
Like the Nyaya School, this School also acknowledges perception, inference, comparison and verbal testimony as the valid sources of knowledge.
Mimamsa
Mimamsa literally means ‘revered thought’ and was originally applied to the interpretation of the Vedic rituals, which commanded highest reverence.
It is also very ancient and Mimamsa Sutra by Jamini was written during 4th century B.C.
A cognition, which apprehends an object, cannot be intrinsically invalid. Memory arises from the impression of a priori cognition.
Kumarila defines valid knowledge is free from causes from defects and which is not contradicted by subsequent knowledge.
A valid cognition must fulfill four conditions.
1. It must not arise from defective causes.
2. It must be free from contradiction. It must be selfconsistent and should not be set aside by subsequent knowledge .
3. Novelty is an essential feature of knowledge (agrhitagrahi). Memory is excluded from valid acknowledge.
4. It must truly represent the object.
Here, all knowledge is valid by itself. It is not validated by any other knowledge. It is not due to any extraneous conditions. A need for explanation is felt only when knowledge fails.
If a rope is mistaken for a snake, the knowledge of the rope snake is invalidated by the subsequent knowledge of the rope. Truth is normal and error is abnormal. Belief is natural and disbelief is an exception.
According to Badrayana, (Uttara Mimiimsa and Vedanta) knowledge comes from the scriptures (Sruti) and other authorities (Smriti). Scripture refers to the Vedas and Smriti to the Bhagavad Gita, Mahabharata and Laws of Manu.
According to Samkya, both the validity (Pramanya) and the invalidity (Apramanya) of knowledge are selfevident.
Whatever manifests itself at any time has all along been hidden there.

Heterodox School’s Views of Knowledge

As we discussed earlier, Jainism and Buddhism did not recognize the authority of Vedas as the orthodox system of philosophy, they are considered as the heterodox schools of philosophy.
Jainism
Jains has critically examined the valid sources of knowledge. Here, knowledge is of two kinds and they are as follows.
1. Pramana: It refers to the knowledge of a thing as it is.
2. Naya or knowledge of a thing in its reflection. It means the standpoint of thought from which we make a statement about a thing. All truth is relative to our standpoint. Partial knowledge of one of the innumerable aspects of a thing is called ‘naya’.
Both Pramana and Naya are essential for the full and true knowledge of a thing.
Jains classify knowledge gained through Pramana
into direct (aparoksa) and indirect (paroksa).
1. Immediate (Aparoksa): Avadhi, Manahparyiiya and Kevala.
2. Mediate (Paroksa): Mati and Shruta.
In immediate knowledge, Avadhi is clarivoyance, Manah-paryaya is telepathy and kevala is omniscience.
Avadhi and manah-paryaya are immediate and limited forms of knowledge, while kevala is unlimited and absolute knowledge.
Mediate knowledge is divided into mati and shruta.
Mati includes both perceptual and inferential knowledge.
Shruta jnana means knowledge derived from authority. It is to be gained from authoritative books and words of great sages. Perusal of authoritative books and listening to the sermons of saints are essential for this kind of knowledge.
Perceptual knowledge is ordinarily called as ‘immediate’, thus admitted to be relatively so by Jainism. Therefore, it is included in mediate knowledge. Pure perception in the sense of mere sensation cannot rank the title of knowledge. It must be given meaning and arranged into order by conception or thought. Perceptual knowledge is therefore regarded as mediate since it presupposes the activity of thought. Mediate knowledge is divided into mati and shruta. Mati includes both perceptual and inferential knowledge.
According to Jaina epistemology indirect knowledge is of five kinds-Smrti (valid knowledge), Pratyabhijna (Recognition), Tarka (logic), Anumana (inference) and Agama (words of reliable people). Here, we can discuss two important aspects. Naya vada means a standpoint of thought from which we make a statement about a thing. All truth is relative to our standpoints. Partial knowledge of one of the innumerable aspects of a thing is called ‘Naya’.
Syad vada or saptabhangi Naya is the most important part of Jaina logic. According to this, we can know only some aspects of reality and so all our judgements are relative. It is a theory of the relativity of knowledge.
Buddhism
In epistemological ideas also we can see the different opinions among the four schools of Buddhism. 1. Yogacara 2. Madhyamika 3. Sautrantika and 4. Vaibhasika Sautrantika says that the external objects are not known through perception. According to Vaibhasika says that the knowledge of the external objects can also be gained through perception.
According to Vaibhasika, the inference of things external to knowledge is self-contradictory. If all the external objects are inferred by their knowledge, then nothing can be known by perception. In the absence of perception there can be no relation of concomitance between the major and the minor premise without which no inference is possible. This is opposed to actual experience. The Vaibhasikas accept the presence of the external things and conceive them as subject to perception. To them by Pramana only direct knowledge is possible. The Pramanas are two types , namely Pratyaksa (perception) and anumana (inferential). Both these Pramanas are known as samyagjnana (right knowledge) and it is by these that all the purusharthas are attained. Pratyaksa is the knowledge devoid of imagination and error. This knowledge is of four types and they are as follows.
1. Indriya jnana: Knowledge through senses.
2. Mano vijnana: Sensual knowledge in the form of samanatara pratyaya after the knowledge through senses.
3. Atma samvedana: It is the manifestation of chitta and its dharmas are like pleasure and pain in their real form.
4. Yogic jnana: It is the ultimate knowledge of the things perceptible through various Pramanas.
Inference is of two types, such as Svartha (for the self) and parartha
(for others). In the former, the linga is inferential, i.e., in the inference there is fire on the hill, the hill is linga and the fire is inferential. In it the linga remains in self side (svapaksa), just as the kitchen. The linga does not remain in the opposite side (vipaksa), e.g., a pool of water, etc.
In fact, Buddhism and Jainism movements were started to reform the Hinduism. The languages spoken by the masses, such as Prakrit and Pali started getting prominence over Sanskrit, a language which was limited to priestly and aristocratic class. The source of both the religion is vedic religion and both and indebted to Upanishads.
Buddhism is centered upon the life and teachings of Gautama Buddha, whereas Jainism is centered on the life and teachings of Mahavira. Buddhism is a polytheistic religion and its main goal is to gain enlightenment. Jainism is also a polytheistic religion and its goals are based on non-violence and liberation the soul.
Buddhism says that This life is suffering and the only way to escape from this suffering is to dispel one’s cravings and ignorance by practising the Eightfold Path.
Jainism suggests to respect all living things. Attain liberation by avoiding and shedding of bad karma which is the cause of rebirths and all sufferings.

Pramana (Source Of Knowledge)

The general science of inference is logic and its aim is to make explicit the rules by which inferences are drawn. Inferences are rule-governed steps from one or more propositions known as premises, to another proposition called conclusion. A deductive inference is one that is intended to be valid, where a valid inference is one in which the conclusion must be true if the premises are true. All other inferences are inductive.
Our discussion is primarily based upon nyaya system.
Vatsayana defines a Pramana as a source or means of valid knowledge. Gautama’ Nyaya Sutra defines perception as an awareness which is (i) produced from the connection between the sense organ and object; (ii) not produced by words; (iii) not deviating from its object, i.e., it is always true and (iv) is of the nature of certainty. There are four factors involved in any knowledge and they are listed below.
1. The subject who knows (Pramata) 2. The object of knowledge (Prameya) 3. The means of valid knowledge (Pramana) 4. The resultant of valid knowledge (Prama) Knowledge can be termed as prama (valid) and aprama
(invalid).
Hence, pramana is valid means of knowledge. It has four important means and they are listed below.
1. Pratyaksa (Perception) 2. Anumana (Inference) 3. Upamana (Comparison) 4. Shabda (Verbal testimony) Here, a causal relation is discerned and ascertained between Prama and pramana on the basis of uniform agreement in presence and absence between the two. The former cannot arise without the latter and hence, it is maintained that the latter is the source or cause of the former.
Different schools of knowledge accept or reject different ones of these methods.
1. All methods are accepted by Mimamsa.
2. Only perception, inference and testimony by Samkhya and Yoga.
3. Only perception and inference by Buddhism and Vaisesika.
4. Only perception by Charvaka.

Pratyaksha (Perception)

It is basically which is before one’s eyes, ‘aksa’ means sense organ and ‘prati’ means the function of each sense organ. Perception is a valid form of knowledge produced by the contact of an object with a sense organ.
It is the first of the five means of knowledge or pramanas, that enable a person to have correct cognitions of the world.
Pratyaksha is of two kinds and they are as follows.
1. Anubhava: Direct perception 2. Smriti: Remembered perception Some schools make a further distinction between in indiscriminate perception (nirvikalpaka), the object is perceived without its distinguishing features.
Indiscriminate perception is important to the followers of the Advaita (Non-dualist) school of Vedanta, for it allows for the liberating perception of brahman (ultimate reality), which is without features. Discriminate perception (savikalpaka), in which the distinguishing features are both observed and recognized. The knowledge arises by contact of sense organs (indriya) with an object. Such contact is not the sole condition of perception, but it is its distinctive feature or extraordinary cause (karana) of perception. The actual process is given below:
1. The self comes into contact with mind (manas) 2. The manas with the senses 3. The senses with the object The function of a sense organ in respect to its own object is described in two ways, such as nature of contact and nature of knowledge.
Sense-object is also the instrumental cause of perception, as it immediately gives rise to the perceptual knowledge of that particular object. The modern school of Nyaya gives a new definition of perception as it is direct or immediate cognition that is not derived through the instrumentality of any other cognition. It applies to all cases of perception, human or divine. Even God’s omniscience has the highest degree of immediacy conceivable.
It excludes inference, analogy and verbal testimony. They have been discussed later as NTA-NET Exam pattern.
It excludes ‘memory’ as well.
Perception is divided into the following two categories.
1. Ordinary (Laukika) 2. Extraordinary (Alaukika) According to later logicians, there are two kinds of verbal testimony as given below.
1. Vaidika or Alukika: It is also known as divine or scripture.
2. Laukika or secular
The former relates to the words of God. The Vedas are created by God and therefore, valid perfectly. The latter relates to the words of trustworthy people. According to Nyayikas, since human beings are not perfect, only the words of trustworthy people can be considered as Laukika Shabda. In ordinary perception, knowledge results from the contact of the sense organs with the external objects (bahya). Extraordinary perception has three distinctions, such as perception of classes (samanyalaksna), complication (jnana laksnana) and intuition (yogaja).

Anumana (Inference)

Etymologically the word ‘Anumana’ indicates after knowledge (anu—after, mana—knowledge). It is second source of valid knowledge. The term anumana
literally means ‘after-knowledge’, i.e., knowledge that follows other knowledge. Inference is defined as the knowledge of an object (lingi) due to a previous knowledge of some sign or mark (linga).
Gautama defines it as a specific form of knowledge preceded by perception. The perception of the invariable relation between the proban (linga) and the probandum (lingi) is a previous perception of such a relation somewhere else. Again, there is a perception of the proban as invariably related to probandum as it exists in the locus.
According to NTA-NET Exam, the structure and kinds of ‘anumana’ have been discussed further also.

Shabda (Verbal Testimony)

According to Nyaya Philosophy, Shabda is the fourth and last valid source of knowledge. Shabda literally means verbal knowledge. The mere combination of words does not provide a valid knowledge.
All verbal statements are not valid. Hence, Gautama defines Shabda Pramana as the statement of a reliable person. In other words, verbal testimony is the communication from a trustworthy person—Who is a trustworthy person (apta) and why is assertion (upadesa) is a testimony (prambna)? Analysing the process of verbal testimony we get the following steps.
First, there is the perception of the words of a sentence uttered by a trustworthy person.
Second, there is the understanding of the meaning of words. This is called the Karana or the special cause of the verbal knowledge. The knowledge of words (padajnana) leads to the knowledge of objects through the function (vyapara) of recalling the meaning of words.
Gautama and Vatsyayana stated in Nyaya school that verbal knowledge is of two kinds:
1. Drustartha or one relating to perceptible objects, that means the sensible object attainable in this world.
2. Adrustartha or that relating to imperceptible objects, that means the super-sensible object, which is attainable to the other world. This is the division of words of the ordinary people and the seers.

Upamana (Comparison)

Upamana is the combination of ‘upa’ and ‘mana’. ‘upa’ means similarity or ‘sadrusya’ and ‘mana’ means cognition. Thus, upamana is the knowledge derived from similarity. It has been defined as the knowledge of relation between a person and its denotation. Upamana is the third source of valid knowledge.
For example, when we tell a city man that a wild cow is an animal like a cow and later on, in a forest, when he sees a wild cow he recognizes it as the wild cow. Then, his knowledge of the wild cow is the outcome of conjunction with the knowledge of the cow.
Hence, the ‘upamana’ is just the knowledge of the relation between a name (here it is the wild cow and the object denoted by that name (the actual wild cow seen in the forest).
Mimansa treats Upamana as analogy. Buddhism does accept comparison as an independent source of valid knowledge.
According to Mimansa, the following two schools have also been identified.

Arthapatti (Presumption)

It is an independent source of knowledge. It is admitted as a distinct pramana which cannot be brought under anumana or sabda.
It consists in the assumption of some unperceived fact in order to explain apparently inconsistent facts.
Let’s take an example of arthapati. Devadatta is alive and he is not present in his house, we presume that he is elsewhere. The essential element in presumption is that a certain fact like Devadatta’s ‘being alive’ and ‘not being present in his house’ is unaccountable without presuming another fact like being outside his house. In presumption, we proceed from the knowledge of something to be explained to the knowledge of that which explains it. The means of presumption (karana) is the knowledge of the inner contradiction (anupatti) and its result is the reconciliation of the contradiction (upapatti).
If Devadatta is fat and he does not eat during day, we presume that he must be eating during night, otherwise the inconsistency between ‘being fat’ and ‘not eating during day’ cannot be resolved.

Anupalabdhi (Non-apprehension – Mimamsa)

According to Kumarila Bhatta and others, non-apprehension as sixth independent source of knowledge consists in the presentative knowledge of negative facts. In other words, negative facts are cognized by a special instrument (karana) called non-apprehension.
Only positive facts are apprehended through positive sources like perception, inference, etc, but negative facts are apprehended through non-apprehension.
For example, the absence of jar on the ground is apprehended through anuplabdhi.
Kumarila argues that the concept of the emptiness of the container inevitably presupposes non-existence.
He also refutes the Nyaya view that non-apprehension is the same as perception or inference.
Negation is never perceived, for there is no senseobject contact in it.

Structure And Kinds Of Anumana (Inference)

Knowledge that comes after perception is inferntial or relational and it is called inference. Anumana, etymologically means ‘secondary proof’. The data for inference are derived from perception and verbal testimony. There are two main groups of inference and they are as follows.
1. Vyapti: It is when universal relation such as between fire and smoke is known.
2. Paksadharmata: Fire is inferred on the hill, where smoke is perceived in it.
Inference is mediate and indirect. That is arranged through the medium of some mark which is called ‘hetu’. This may be explained with the help of the typical example of inference, the presence of fire on the perception of smoke. When one sees smoke on distant hill one remembers one’s experience of the universal concomitance (Vyapti) between smoke and fire and concludes that there is fire on the distant hill. Thus, we can say that
1. This hill has fire (pratijna) 2. Because it has smoke (hetu) 3. Whatever has smoke has fire, for example, an oven (udaharana) 4. This hill has smoke which is invariably associated with fire (upanaya) 5. Therefore, this hill has fire (nigamana) The first, the pratijna, is the logical statement which is to be proved. The second is hetu or reason which states the reason for the establishment of the proposition. The third is udaharana which the universal concomitance together with example. The fourth is upanaya or application of the universal concomitance to the present case. The fifth is nigamana or conclusion drawn from the preceding propositions. These five members of Indian syllogism are called Avayavas.
In the Aristotelian syllogism, the character which is inferred (fire) is called sadhya; the mark on the strength of which the character is inferred is the hetu (smoke); the subject where the character is inferred is paksa (hill). The three terms correspond to the major, the middle and the minor terms Linga paramarsa: The Nyaya syllogism has five terms.
Among them, middle term works as a bridge between the major and the minor terms. Therefore, the middle term has main responsibility to prove a syllogism valid or invalid. How a middle term is related to major term is linga-paramarsha. There are five characteristics of a middle term.

Vyapati (Invariable Relation)

The word ‘vyâpti’ literally means ‘the state of pervasion.’ It implies a correlation between two facts, of which one is pervaded (vyâpya), and the other pervades (vyâpaka). A fact is said to pervade another when it always accompanies the other. A fact is said to be pervaded by another when it is accompanied by the other. In the given example, smoke is pervaded by fire, since it is always accompanied by fire. But while all smoky objects are fiery, all fiery objects are not smoky, e. g., the red hot iron ball. Thus, vyâpti is a relation of invariable concomitance between middle term and the major term. Without the definite knowledge of such a relation, our inference of fire is impossible in spite of the perception of smoke.
A vyapti may be of two types and they are as follows.
1. Samavyâpti
2. Asamavyâpti
A vyâpti between terms of equal extension is called samavyâpti or equipollent concomitance, for example ‘nameable’ and ‘knowable’. Whatever is nameable is knowable and again whatever is knowable is nameable.
Here, we can infer either of the term from the other.
On the otherh and a vyâpti between terms of unequal extension is called asamavyâpti. Fire is present in all cases wherever smoke is present, but the reverse is not true. The Naiyayikas maintain that there are five ways or methods for the establishment of vyâpti. They are the following:
1. Anvaya or agreement in presence: Vyâpti is a relation of agreement in presence (anvaya) between two things.
2. Vyatireka or agreement in absence: The hetu and the sâdhya should agree in being absent together.
3. Vyabhicaragraha: We do not observe any contrary instance in which one of them is present and the other is absent. That is, they must be related to each other.
4. Upâdhinirasa or elimination of condition:
Vyâpti is an unconditional relationship which is universal and necessary. An adventitious condition may vitiate the natural and invariable relation between hetu and sâdhya.
5. Tarka or hypothetical reasoning: Tarka is an indirect method to get the vyâpti. All the methods mentioned above are direct methods. Ratiocination is the process of thinking about something in a logical way for the to establish the vyâpti.
6. Sâmânyalakaa pratyaka: Sâmânyalakaa pratyaka
is an extraordinary perception. They maintain that when we perceive an individual case, we also perceive all the actual and possible instances of fire and smoke.

Hetvabhas (Fallacies of Inference)

In Indian logic a fallacy is called hetvahasa. It means that middle term appears to be a reason but is not a valid reason. All fallacies are material fallacies. We have mentioned the five characteristics of a valid middle term. When these are violated, we have fallacies.
Five kinds of fallacies are recognized and they are as follows.
1. Assiddha or sadhyasama: This is the fallacy of unproved middle.
2. Savyabhicara: This is the fallacy of irregular middle.
3. Satpratipaksa: Here, the middle term is contradicted by another middle term.
4. Badhita: It is the non-inferentially contradicted middle.
5. Viruddha: It is the contradictory middle. Though there is a variance between the six orthodox schools regarding the sources of knowledge, it is a well-accepted fact that all schools have acknowledged Pratyaksa, Anumana and Shabda as valid sources of knowledge. The knowledge through sense experience is considered to be the basic source even in other pramnas for further evidences and validation.

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